306edo: Difference between revisions

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~~The '''306 equal division''' divides the octave into 306 equal parts of 3.9216 cents each, and thereby~~ provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[~~Patent_val|~~patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo|31\53]] and before [[665edo|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].

306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). In the 7-limit the patent val tempers out [[6144/6125]], whereas 306c tempers out [[16875/16807]]. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo|31\53]] and before [[665edo|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].

306edo provides an excellent approximation of [[Well temperament#Historical well temperaments|Valotti temperament]] due to its representation of the [[Pythagorean comma]] as 6 steps.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 306 factors into {{factorization|306}}, 306edo has subset edos {{EDOs| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}.

[[Category:3-limit record edos|###]]

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-The '''306 equal division''' divides the octave into 306 equal parts of  3.9216 cents each, and thereby provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[Patent_val|patent val]] tempers out 78732/78125, whereas the alternative 306c val tempers out 32805/32768. In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo|31\53]] and before [[665edo|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
+{{Infobox ET}}
+{{ED intro}}
+edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the [[patent val]] [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]), whereas the alternative 306c val tempers out 32805/32768 ([[schisma]]). In the 7-limit the patent val tempers out [[6144/6125]], whereas 306c tempers out [[16875/16807]]. 306 is the denominator of 179\306, the continued fraction convergent after [[53edo|31\53]] and before [[665edo|389\665]] in the sequence of continued fraction approximations to to log<sub>2</sub>(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as [[612edo]].
+edo provides an excellent approximation of [[Well temperament#Historical well temperaments|Valotti temperament]] due to its representation of the [[Pythagorean comma]] as 6 steps.
+=== Prime harmonics ===
+{{Harmonics in equal|306|prec=3}}
+=== Subsets and supersets ===
+Since 306 factors into {{factorization|306}}, 306edo has subset edos {{EDOs| 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153 }}.
+[[Category:3-limit record edos|###]] <!-- 3-digit number -->